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Question

Two pipes A & B would fill a tank in 20 & 30 minutes respectively. Both pipes being open, find when A must be turned off so that tank may be just filled in 15 minutes.

After 10 minutes

After 20 minutes

After 15 minutes

None

ANSWER : 1

Descrption

<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">Let the time be T minutes after which pipe A need to turned off. Both of the pipes remain open together only for T minutes.</span></p>
<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">Pipe A fills 1/20 of the tank in 1 minute.</span></p>
<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">Pipe B fills 1/30 of the tank in 1 minute</span></p>
<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">Together</span><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">&nbsp;</span><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">in 1 minute</span><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">&nbsp;they fill (1/20  +  1/30 = 1/12) of the tank.</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">Together in T minutes they fill  =  T/12 of the tank</span></p>
<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">In (15 - T) minutes, pipe B alone can fill  =  (15 - T)/30 of the tank</span></p>
<p><span style = "box - sizing: border - box; font - size: 18px; color: #212529; font - family: bangla, sans - serif; text - align: justify; background - color: #ffffff;">Now,&nbsp;</span><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">T/12   +  &nbsp;</span><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">(15 - T)/30  =  1</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">or,&nbsp; {15T   +   6(15 - T)}/180  =  1</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">or, (15T   +   90  -  6T) / 180  =  1</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">or,&nbsp; 9T  =  180  -  90</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">or,&nbsp; 9T  =  90</span></p>
<p><span style = "background - color: #ffffff; color: #212529; font - family: bangla, sans - serif; font - size: 18px; text - align: justify;">So, T  = &nbsp;<strong>10 minutes</strong></span></p>

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